224 
Fishery Bulletin 111(3) 
Table 3 
Final generalized additive models (GAMs) for 8 species of reef fishes in our study. Data were obtained from 2 sampling pro- 
grams in the southeastern U.S. Atlantic: the Marine Resources Monitoring, Assessment, and Prediction Program (1990-2011) 
and the Southeast Fishery-independent Survey (2010-11). Binomial GAMs were constructed with presence-absence data, 
and Gaussian GAMs were constructed with only positive catch. The best model for each species was the one with the low- 
est unbiased risk estimator (binomial GAM) or generalized cross validation (Gaussian GAM) scores (see the Materials and 
methods section for full descriptions). A/=number of samples from chevron traps that were included in each model. Dev. exp.= 
the percentage of deviance explained by each model, ex means that the covariate was excluded from the final model, gi... 
g 7 are nonparametric smoothing functions, f= a categorical function, soa&=soak time, fishacc= fish accumulation, year= year, 
doy= day of the year, fat=latitude, depth= bottom depth, temp =bottom temperature, and fod=time of the day. Estimated degrees 
of freedom and statistical significance are 
shown for each term: 
*=P<0.10, 
**=P< 0.05, * 
**=P<0.01. 
Model and species 
N 
Dev. exp. 
gx (soak) g 2 (fishacc) 
f x (year) 
g 3 (doy) 
gi(lat) 
g^depth) 
gs(temp) 
gfitod) 
Binomial GAM 
Bank Sea Bass 
8530 
28.8 
ex 
3.0*** 
21*** 
8.6*** 
8.1*** 
8.9*** 
6.3 
8.3*** 
Black Sea Bass 
8530 
63.6 
ex 
3.0*** 
21*** 
2.6**’ 
8.6*** 
8.2*** 
g ^*** 
1.0** 
Gray Triggerfish 
8530 
20.6 
5.5*** 
3.0*** 
21*** 
8.9*** 
8.8*** 
5.8*** 
4.8*** 
8.1 
Red Porgy 
8530 
27.0 
1.6* 
3.0*** 
21*** 
8.0*** 
8.9*** 
rj g*** 
8.5*** 
5.1" 
Sand Perch 
8530 
37.5 
1.7*** 
6.8*** 
21 *** 
ex 
7.0*** 
rj g*** 
6.1 
1.0*** 
Stenotomus spp. 
8530 
61.4 
3.3*** 
7.4*** 
2!*** 
ex 
5.9*** 
6.0*** 
rj q*** 
8.1*“ 
Tomtate 
8530 
46.9 
5.6*** 
8.2*** 
2 2 *** 
2.8’** 
8.9*** 
8.3*** 
7.1**’ 
2.0* 
Vermilion Snapper 
8530 
38.0 
1.6 
8.6*** 
21*** 
1.0*** 
g 2*** 
rj ^ *** 
7.!*** 
8.2*** 
Gaussian GAM 
Bank Sea Bass 
2571 
22.1 
ex 
2.9*** 
2!*** 
8.9*** 
8.2*** 
8.5*’* 
6.8*** 
3.9*** 
Black Sea Bass 
3476 
64.4 
ex 
8.1*** 
21 ‘** 
rj q*** 
8.6*** 
7.2*** 
2 g*** 
4.8“* 
Gray Triggerfish 
2244 
18.9 
2.3** 
2.9*** 
21 *** 
1.0*** 
7.5*** 
7.4*** 
1.0 
7.7*** 
Red Porgy 
3104 
21.4 
3.4’ 
2.0*** 
21 *‘* 
2.1 
8.8*** 
8.8*** 
2.2 
1.0*’ 
Sand Perch 
1568 
26.5 
ex 
2.8*** 
21*** 
5.3 
8.9*** 
2.7*** 
3.4* 
ex 
Stenotomus spp. 
1733 
48.6 
4.0* 
4.0*** 
21 *** 
1.0 
8.8*** 
7.9*** 
5.4** 
4.8** 
Tomtate 
3437 
51.2 
ex 
7.0*** 
21*** 
6.2** 
8.8*** 
8.8*** 
7.7*** 
4.4** 
Vermilion Snapper 
2240 
36.1 
ex 
6.4*** 
2!*** 
ex 
8.0*** 
5.4*** 
1.0 
ex 
which is effectively a rescaled AIC approach that is 
well suited for binomial models (Wahba, 1990). For the 
positive-catch GAM submodels, we used generalized 
cross validation (GCV; a measure of the out-of-sample 
prediction mean squared error) to select the most par- 
simonious combination of predictor variables. For each 
approach, the model for each species with the smallest 
UBRE or GCV score was selected as the best model 
in that particular model set. In addition, we evaluated 
the model diagnostics for each final model selected by 
UBRE or GCV. In all cases, residuals in final models 
met assumptions of normality and constant variance. 
All models were coded and analyzed in R, 1 vers. 2.14.1 
(R Development Core Team, 2011) with the mgcv li- 
brary, vers. 1.7-13 (Wood, 2008). 
We used 2 methods to test for the presence or ab- 
sence of spatial autocorrelation, which is the situation 
where samples near one another are often more simi- 
lar than 2 samples farther apart. First, we developed 
generalized additive mixed models (GAMMs) for each 
species with the same covariates as the GAM models 
1 Mention of trade names or commercial companies is for identifica- 
tion purposes only and does not imply endorsement by the National 
Marine Fisheries Service, NOAA. 
presented previously. GAMMs are spatially explicit 
regression models that allow for spatially correlated 
error distributions (Venables and Ripley, 2002). Us- 
ing positive-catch data, we found that the coefficient 
of multiple determination ( R 2 ) and parameter signifi- 
cance values from the GAMMs were nearly identical to 
GAM model results for all 8 species. Binomial GAMMs 
built on presence-absence data never converged for any 
species. Second, we developed semivariograms for each 
species for each year using the R package geoR, vers. 
1.7-2 (R Development Core Team, 2011). There were 
no consistent patterns in the relationship between the 
semivariance of the model residuals and distance be- 
tween sampling points, indicating negligible spatial 
autocorrelation in the residuals. 
The overall influence of soak or fishacc on reef fish 
catch was calculated as the product of the binomial 
and positive-catch submodels, and the variance of the 
overall model was estimated with a bootstrapping ap- 
proach. We resampled the predictions (N= 10,000) for 
both submodels at average values of all other predictor 
variables according to the pointwise estimates of error 
that were assumed to be distributed normally. For the 
combined (overall) predictions, we multiplied the simu- 
lated point estimates of error for each submodel. The 
